Find the Greatest 6 Digit Number Exactly Divisible by 24, 15 and 36

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.

Step 1: Find the LCM of 24, 15 and 36

Prime factorisation:

24 = 2³ × 3

15 = 3 × 5

36 = 2² × 3²

LCM = 2³ × 3² × 5

LCM = 360

Step 2: Find the Greatest 6 Digit Number

The greatest 6 digit number = 999999

Step 3: Find the Required Number

Required number = 999999 − (999999 mod 360)

999999 ÷ 360 gives remainder 279

Required number = 999999 − 279

Required number = 999720

Final Answer

∴ The greatest 6 digit number exactly divisible by 24, 15 and 36 is 999720.

Conclusion

Thus, by finding the LCM of 24, 15 and 36 and adjusting the greatest 6 digit number accordingly, we obtain the required answer as 999720.